new directions in design of binary matrices for spn block ciphers

. di usion layer plays an important role in a block cipher.some block ciphers, such as aria, camellia, and skinny use binary matrices as di usion layers which can be e ciently implemented in hardware and software. in this paper, the goal is to propose some new binary matrices with suitable values for number of active s-boxes for r rounds. firstly, some new 16 16 matrices are proposed whose software implementation are better than corresponding one for aria block cipher. also, the values for minimum number of active s-boxes for these matrices are greater than corresponding values for aria block cipher for r > 5. to design 32 32 matrices, a structure with a special form is proposed. using this structure, a 32 32 binary matrix is proposed which guarantees at least 48 active s-boxes for 8 rounds of an spn structure with this matrix as its di usion layer. by extending this structure, a 32 32 nonbinary matrix is presented which results in at least 60 active s-boxes after 8 rounds.